The EU was very insistent on the UK paying back its obligations to the EU after leaving the Union, as a condition for negotiating a favorable trade deal. But would the UK have to pay back anything if it leaves the EU without a deal of any kind on March 29th?
The short answer is that people don't all agree whether the UK has any legal commitments to the EU until a withdrawal agreement is ratified, but the House of Lords (and possibly the UK government) have been advised not.
In a House of Lords report dated 4th March 2017 the position was developed which was summarised in the following paragraphs:
The budget is going to be a contentious early issue during the UK’s negotiations over leaving the EU. It is crucial for both parties. The UK provides approximately 12% of the resources available to the EU budget, and is also a significant net contributor. The removal of the UK’s payments into the budget will require the other EU Member States to agree either to pay more into the budget, or draw less from it. Neither option is without difficulty, and those difficulties may colour the wider Brexit negotiations. The Government will have to consider its stance on continued budgetary contributions in the light of its impact on the wider negotiations, and the economic and political implications will need to be set against one another. The Government has stated that it is open to making payments towards specific programmes in order to cement a cooperative future relationship with the EU but there are already demands from the EU, for much wider contributions.
However, the strictly legal position of the UK on this issue appears to be strong. Article 50 provides for a ‘guillotine’ after two years if a withdrawal agreement is not reached unless all Member States, including the UK, agree to extend negotiations. Although there are competing interpretations, we conclude that if agreement is not reached, all EU law—including provisions concerning ongoing financial contributions and machinery for adjudication—will cease to apply, and the UK would be subject to no enforceable obligation to make any financial contribution at all. This would be undesirable for the remaining Member States, who would have to decide how to plug the hole in the budget created by the UK’s exit without any kind of transition. It would also damage the prospects of reaching friendly agreement on other issues. Nonetheless, the ultimate possibility of the UK walking away from negotiations without incurring financial commitments provides an important context.
The primary alternative interpretation holds that exercise of Article 50 doesn't rule out Article 70 of the Vienna Convention on the Law of Treaties, which reads:
Unless the treaty otherwise provides or the parties otherwise agree, the termination of a treaty under its provisions or in accordance with the present Convention:
releases the parties from any obligation further to perform the treaty;
does not affect any right, obligation or legal situation of the parties created through the execution of the treaty prior to its termination.
This all gets a little bit more complicated, since the dispute may or may not need to be settled by the European Court of Justice, which may or may not have the jurisdiction to make a decision after a no deal Brexit.
'Have to' is ill-defined. Just like a regular person, it could decide not to pay. The question is what the consequences of not paying are.
Rather than look at what the EU could do in retaliation, it's interesting to look at the UK itself. The UK has said that it wants to negotiate trade deals with other countries. Since those deals are not yet negotiated, those other countries will look at how the UK deals with its current trading partners. In particular, not making payments you have previously committed to will make one look untrustworthy (just like a regular person not paying their bills).
Given that the UK wants to make these trade deals, they do have a strong incentive to make these payments or at least settle the issue with the EU on good terms.
So do they have to pay? Possibly not. Is it in their interest to pay? Yes. Would it hurt their negotiating position with third countries if they left without paying and the EU publicly challenged them? Definitely.
As pointed out in the comments, this might seem like semantics. The reason it might hurt the UK's future negotiating position is that they have signed a regulation (the Multiannual Financial Framework 2014-2020) which as the name suggests is a budget that ends in 2020.
The UK can argue that it is not legally required to pay its contributions under that regulation because it's no longer bound by EU law, however, that does not take away the fact that they committed to paying.
To support this, I cite a passage from Channel 4's 'Can we avoid paying the £39 billion Brexit divorce bill?' FactCheck in which Professor Begg at The LSE responds to the report in the House of Lords that argues the UK needn't pay:
“The logic goes that when you leave an entity you no longer have a financial commitment” he says. But “the contrary view is that we signed a regulation in 2013 that sets the Medium-Term Budgetary Framework that ends in 2020.”
Hang on, “Medium-Term Budgetary Framework”? EU member states commit to fund projects (like infrastructure investment) in seven-year cycles. We are trying to leave the EU before the end of the current one.
The £39 billion divorce bill is the figure Westminster and Brussels have arrived at to cover the outstanding budget contributions we committed to paying in 2013, and which we would have been paying in 2019 and 2020 were we not leaving the EU. There are also some commitments (like pension contributions) that go beyond 2020, which will be settled in the divorce bill.
Professor Begg says that because the UK signed the 2014-2020 Framework, “you could argue we’re bound to that.”
The EU has now implemented some unilateral preparedness measures which are aimed at continuation of EU services for British citizens provided the UK honors its financial commitments. To quote from today's press release on these preparedness measures illustrating how the EU might compel the UK to honor its commitments:
UK beneficiaries of EU funding would continue to receive payments under their current contracts, provided that the United Kingdom continues to honour its financial obligations under the EU budget. This issue is separate from the financial settlement between the European Union and the United Kingdom.
Yes, but it's wrong to see it as "pay back". It's not about money given to the UK by the EU which the EU now wants back.
It's about commitments for future payments which were made by all EU countries, including the UK. A noteworthy example is pensions for EU staff. EU staff has rights to those pensions (just like anyone else); not now, but sometime in the future.
Now, I don't know what recourse the EU has if the UK doesn't fulfill its obligations, but the obligations are still there.